Hong-Jian's Tips on Calculus

 

 

 

Words From Hong-Jian:

 

This is the area where you may find something arisen from working on the problems in Calculus. Now it is in the beginning stage. I hope this will grow and will offer Calculus learning students certain help outside the classroom. Students are the most important for making this place to grow and to become a spot where the Calculus learning students would find helpful. Please send your feedback and suggestions to me at hjlai@math.wvu.edu and I will appreciate your comments very much.

 

 

 

 

 

 

 

 

 

 

Click the Tip to see if that will be helpful for you. All these reviews are in PDF format, which may require an Acrobat Reader to view them. If you do not have an Acrobat Reader, you can download one free by clicking Acrobat Reader.

 

 

 

 

 

 

 

 

 

 

 

 

 

Tip

        Operations involving 3D vectors

        Compute the angle between two vectors

        Compute component of a vector a along a vector b

 

 

Tip

        Write the equation of a sphere

        Compute the center and the radius of a sphere

        Determine if two vectors are parallel or perpendicular

 

Tip

        Determine if three points are coline

        Compute the direction cosines of a vector

        Verify the triangle inequality

 

 

Tip

        Compute the cross (vector) product of two vectors

        Find unit vectors perpendicular to two given vectors

        Compute areas

        Compute volumes

 

Tip

        Compute the equations of a line in space

 

Tip

        Determine the relationship of two lines

 

Tip

        Write the equation of a plane

 

Tip

        Determine the relationship of a line and a plane

        Find the angle between two planes

 

Tip

        Write equations of a line as intersections of two planes

 

 

Tip

        Determine the relationship of a line and a plane (in parametric equations)

        Determine the relationship of two planes (in parametric equations)

 

 

Tip

        Show a parametric curve is lying on a surface

        Evaluate vector functions

        Find velocity and acceleration vectors

        Compute the integrals of vector functions

 

 

Tip

        Compute the derivative of vector functions

        Find position vectors

        Show facts on vectors

 

 

Tip

        Compute the arc length of curves

        Compute the curvature of a curve

        Search the place with maximum curvature

 

Tip

        Compute unit tangent and unit normalvectors, tangential and normal components

 

Tip

        Write an equation for the surface generated by revolving a plane curve around an axis

 

Tip

        Determine the projection of the intersection curve of two surfaces

 

Tip

        Convert from one coordinate system to another

 

Tip

        Convert equations from one coordinate system to another, I

 

Tip

        Convert equations from one coordinate system to another, II

 

Tip

        Determine the largest possible domain of a function

 

Tip

        Use limit laws to evaluate limits

        Determine if the limit does not exist

 

Tip

        Compute partial derivatives

        Find an equation of the tangent plane

 

Tip

        Find the points with horizontal tangent planes

        Find the lowest or highest point of surfaces

 

Tip

        Find the maximum and minimum values of f(x,y) over a region R

 

Tip

        Compute partial derivatives with Chain Rule

 

Tip

        Compute the Gradient Vector

        Compute the directional derivative of a function

 

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        Find the maximum directional derivatives of a function at a given point

        Find tangent planes with normal gradient vector

 

Tip

        Find and classify critical points

 

Tip

        Compute the (double integral) Riemann sum

        Evaluate double integrals over rectangular regions

 

Tip

        Evaluate double integrals over general regions (and change order of integration)

 

Tip

        Compute area and volume by evaluating double integrals

 

Tip

        Compute double integrals in polar coordinates

 

Tip

        Compute iterated triple integrals

 

Tip

        Compute integrals in cylindrical coordinates

 

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        Compute integrals in spherical coordinates

 

Tip

        Compute the mass and the centroid and the moments of a solid

 

Tip

        Compute the line integrals

 

Tip

        Compute the line integrals in conservative fields and search for potential functions

 

Tip

        Compute integrals using Green's Theorem

 

 

 

 

 

If you think that this webpage has been useful in helping your study, please send a message to hjlai@math.wvu.edu to acknowledge it. Your email will support the further development of this and other similar assistance for Calculus studying students.

 

 

 

 

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